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to obtain the solution in a series Example. Use Adomian decomposition method to solve the following linear partial differential equations: ux+y=x+y, i. ii. Ux-Uy = 0, u(0,y) = 0, u(x, 0) = 0. iii. xux + y = 3u, u(0,y) =y, u(x,0) = x. u(0,y) = 0, u(x, 0) = x². iv. ux + y + z = u, U₁t + Uxx = 0, = ut uxx + sin(x), V. vi. vii. viii. Uxx = Utt + U₁ - u Utt = Uxx + Uyy - 7u, u(0,y,z)=1+ e + e², u(x,0,2)=1+ e + u(x,y,0)=1+ex +ex. u(x, 0) = -ex, u(x, 0) = 0. u(x, 0)=sin(x), u(x, 0) = sin(x). u(x, y, 0) = sin(x) sin(y), u(x, y, 0) = 0. u(0,t) = ezt,ux (0,t) = e−2. Example. Solve the following linear Goursat problem Uxy - u = -x, u(x, 0) = x+ex, u(0,y) = e, u(0,0) = 1.

to obtain the solution in a series Example. Use Adomian decomposition method to solve the following linear partial differential equations: ux+y=x+y, i. ii. Ux-Uy = 0, u(0,y) = 0, u(x, 0) = 0. iii. xux + y = 3u, u(0,y) =y, u(x,0) = x. u(0,y) = 0, u(x, 0) = x². iv. ux + y + z = u, U₁t + Uxx = 0, = ut uxx + sin(x), V. vi. vii. viii. Uxx = Utt + U₁ - u Utt = Uxx + Uyy - 7u, u(0,y,z)=1+ e + e², u(x,0,2)=1+ e + u(x,y,0)=1+ex +ex. u(x, 0) = -ex, u(x, 0) = 0. u(x, 0)=sin(x), u(x, 0) = sin(x). u(x, y, 0) = sin(x) sin(y), u(x, y, 0) = 0. u(0,t) = ezt,ux (0,t) = e−2. Example. Solve the following linear Goursat problem Uxy - u = -x, u(x, 0) = x+ex, u(0,y) = e, u(0,0) = 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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to obtain the solution in a series Example. Use Adomian decomposition method to solve the following linear partial differential equations: ux+y=x+y, i. ii. Ux-Uy = 0, u(0,y) = 0, u(x, 0) = 0. iii. xux + y = 3u, u(0,y) =y, u(x,0) = x. u(0,y) = 0, u(x, 0) = x². iv. ux + y + z = u, U₁t + Uxx = 0, = ut uxx + sin(x), V. vi. vii. viii. Uxx = Utt + U₁ - u Utt = Uxx + Uyy - 7u, u(0,y,z)=1+ e + e², u(x,0,2)=1+ e + u(x,y,0)=1+ex +ex. u(x, 0) = -ex, u(x, 0) = 0. u(x, 0)=sin(x), u(x, 0) = sin(x). u(x, y, 0) = sin(x) sin(y), u(x, y, 0) = 0. u(0,t) = ezt,ux (0,t) = e−2. Example. Solve the following linear Goursat problem Uxy - u = -x, u(x, 0) = x+ex, u(0,y) = e, u(0,0) = 1.
Transcribed Image Text:to obtain the solution in a series Example. Use Adomian decomposition method to solve the following linear partial differential equations: ux+y=x+y, i. ii. Ux-Uy = 0, u(0,y) = 0, u(x, 0) = 0. iii. xux + y = 3u, u(0,y) =y, u(x,0) = x. u(0,y) = 0, u(x, 0) = x². iv. ux + y + z = u, U₁t + Uxx = 0, = ut uxx + sin(x), V. vi. vii. viii. Uxx = Utt + U₁ - u Utt = Uxx + Uyy - 7u, u(0,y,z)=1+ e + e², u(x,0,2)=1+ e + u(x,y,0)=1+ex +ex. u(x, 0) = -ex, u(x, 0) = 0. u(x, 0)=sin(x), u(x, 0) = sin(x). u(x, y, 0) = sin(x) sin(y), u(x, y, 0) = 0. u(0,t) = ezt,ux (0,t) = e−2. Example. Solve the following linear Goursat problem Uxy - u = -x, u(x, 0) = x+ex, u(0,y) = e, u(0,0) = 1.
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